<?php

/**
 * @package JAMA
 *
 *    Cholesky decomposition class
 *
 *    For a symmetric, positive definite matrix A, the Cholesky decomposition
 *    is an lower triangular matrix L so that A = L*L'.
 *
 *    If the matrix is not symmetric or positive definite, the constructor
 *    returns a partial decomposition and sets an internal flag that may
 *    be queried by the isSPD() method.
 *
 * @author Paul Meagher
 * @author Michael Bommarito
 * @version 1.2
 */
class CholeskyDecomposition
{
	/**
	 *    Decomposition storage
	 * @var array
	 * @access private
	 */
	private $L = array();
	
	/**
	 *    Matrix row and column dimension
	 * @var int
	 * @access private
	 */
	private $m;
	
	/**
	 *    Symmetric positive definite flag
	 * @var boolean
	 * @access private
	 */
	private $isspd = true;
	
	/**
	 *    CholeskyDecomposition
	 *
	 *    Class constructor - decomposes symmetric positive definite matrix
	 * @param mixed Matrix square symmetric positive definite matrix
	 */
	public function __construct($A = null)
	{
		if ($A instanceof Matrix) {
			$this->L = $A->getArray();
			$this->m = $A->getRowDimension();
			
			for ($i = 0; $i < $this->m; ++$i) {
				for ($j = $i; $j < $this->m; ++$j) {
					for ($sum = $this->L[ $i ][ $j ], $k = $i - 1; $k >= 0; --$k) {
						$sum -= $this->L[ $i ][ $k ] * $this->L[ $j ][ $k ];
					}
					if ($i == $j) {
						if ($sum >= 0) {
							$this->L[ $i ][ $i ] = sqrt($sum);
						} else {
							$this->isspd = false;
						}
					} else {
						if ($this->L[ $i ][ $i ] != 0) {
							$this->L[ $j ][ $i ] = $sum / $this->L[ $i ][ $i ];
						}
					}
				}
				
				for ($k = $i + 1; $k < $this->m; ++$k) {
					$this->L[ $i ][ $k ] = 0.0;
				}
			}
		} else {
			throw new PHPExcel_Calculation_Exception(JAMAError(ARGUMENT_TYPE_EXCEPTION));
		}
	}
	
	/**
	 *    Is the matrix symmetric and positive definite?
	 *
	 * @return boolean
	 */
	public function isSPD()
	{
		return $this->isspd;
	}
	
	/**
	 *    getL
	 *
	 *    Return triangular factor.
	 * @return Matrix Lower triangular matrix
	 */
	public function getL()
	{
		return new Matrix($this->L);
	}
	
	/**
	 *    Solve A*X = B
	 *
	 * @param $B Row-equal matrix
	 * @return Matrix L * L' * X = B
	 */
	public function solve($B = null)
	{
		if ($B instanceof Matrix) {
			if ($B->getRowDimension() == $this->m) {
				if ($this->isspd) {
					$X = $B->getArrayCopy();
					$nx = $B->getColumnDimension();
					
					for ($k = 0; $k < $this->m; ++$k) {
						for ($i = $k + 1; $i < $this->m; ++$i) {
							for ($j = 0; $j < $nx; ++$j) {
								$X[ $i ][ $j ] -= $X[ $k ][ $j ] * $this->L[ $i ][ $k ];
							}
						}
						for ($j = 0; $j < $nx; ++$j) {
							$X[ $k ][ $j ] /= $this->L[ $k ][ $k ];
						}
					}
					
					for ($k = $this->m - 1; $k >= 0; --$k) {
						for ($j = 0; $j < $nx; ++$j) {
							$X[ $k ][ $j ] /= $this->L[ $k ][ $k ];
						}
						for ($i = 0; $i < $k; ++$i) {
							for ($j = 0; $j < $nx; ++$j) {
								$X[ $i ][ $j ] -= $X[ $k ][ $j ] * $this->L[ $k ][ $i ];
							}
						}
					}
					
					return new Matrix($X, $this->m, $nx);
				} else {
					throw new PHPExcel_Calculation_Exception(JAMAError(MatrixSPDException));
				}
			} else {
				throw new PHPExcel_Calculation_Exception(JAMAError(MATRIX_DIMENSION_EXCEPTION));
			}
		} else {
			throw new PHPExcel_Calculation_Exception(JAMAError(ARGUMENT_TYPE_EXCEPTION));
		}
	}
}